The writ of trespass and its various confusing variations are things that you were forced to read about at some point during law school, for reasons that were – and probably remain – not very clear. Most likely, your professor cared no more about teaching it than you did about learning it; most law professors pay no more attention to legal history than do most lawyers. Trespass is so important that they couldn’t ignore it completely, so they mentioned it and then skipped quickly to something more interesting and relevant, like "Law of Outer Space: Are Martians Covered by the ADA?"
Here is the quick and dirty version of what you missed:
“Trespass” was originally a generic word for a “wrong” – as in the Biblical “Forgive us our trespasses” – including legal wrongs. Gradually, other terms and categories developed to describe particular types of wrongs; in legal usage “trespass” continued to be a catch-all term for wrongs that did not fit into some other, more specific category. Its meaning then narrowed to the point where it was itself a rather specific category: it came to mean what we would call certain types of torts. As stated in the writs of trespass, it included:
Trespass quare clausum fregit: a wrong “because he broke the close”, i.e., trespassed (in the modern sense) on the plaintiff’s real property;
Trespass de bonis asportatis: a wrong “concerning goods carried away”; what we would call conversion of personal property;
Trespass vi et armis: a wrong “by force and arms,” e.g. assault.
The writ of trespass was developed before 1250 as a sort of civil version of a felony. What the writs of trespass had in common was that they involved forcible, or at least intentional, action that directly resulted in injury. Lawyers tried to fit their cases into one of these writs since, if they could not, they had no case. While courts allowed some flexibility in their use, the basics had always to apply: direct harm forcibly caused. So, when a landholder chopped down a tree and it landed on his neighbor, that could be squeezed into a trespass writ; but where the tree landed on the road and a passerby stumbled over it after dark, there was no direct injury and therefore no trespass.
To correct this problem a statute of 1285 allowed writs of trespass to be issued in consimili casu, "in similar cases." Non-specific writs of trespass could now be obtained if the fact situation were similar to those covered by traditional writs (as those had come to be interpreted by the courts) even if the injuries were not direct. A trespass in consimili casu was referred to as “trespass on the case” or simply “case.” The freedom of action allowed by actions on the case was not quickly taken advantage of and it is not until Edward III’s reign (1327-1377) that we begin to see significant numbers of writs called “trespass” that cannot fit the traditional definitions.
But while giving, the writ also took away. Under the writ of trespass the plaintiff did not need to prove actual harm; the act itself, because of its forcefulness and directness, was enough to establish injury. But one who could not claim direct harm could not simply prove the act: actions on the case required proof of injury.
It is easy enough to see that writs on the case lead eventually to the negligence action. Notice also, though, that the writs of trespass account for the distinction between negligence and intentional torts and for differences between them. Assault, battery, false imprisonment, trespass to land, and trespass to chattels are all traceable to the writs of trespass (not case). It is still generally true that they do not require proof of injury; a plaintiff may prove specific injury but can obtain at least nominal damages if he does not. And the intent required is generally only the intent to do the act. These torts are rather mechanical in their operation because the writ of trespass was as well. More modern intentional torts, such as defamation, require proof of intent to cause harm, and even negligence presumes awareness that doing the act could cause harm. (What we would call defamation actions existed in the middle ages but were handled by ecclesiastical courts.)
The other interesting outgrowth of the writ on the case was the writ of assumpsit. This became the standard way to enforce contracts. Traditional contract writs only applied to contracts under seal; for other contracts lawyers needed something new. So they brought a writ of trespass on the case, alleging that the defendant had undertaken (assumpsit) to do something and had harmed the plaintiff by not doing so, or by doing so incorrectly. The idea of an undertaking was pleaded in order to explain what we would call the plaintiff’s justifiable reliance on the defendant to do the thing undertaken.
So, to sum up: “trespass” once referred to all wrongs but came to mean those set out in a certain type of writ; that writ was the ancestor of personal actions, both tort and contract. That’s why it was important.